1. PLOT GRAPHICS

1. GRADIENT METHOD

   2.1. Constant step method

   2.2. Dynamic step method

   2.3. Fastest Gradient Descent

1. CONTOUR

1. CONTOUR AND SCATTER PLOT OF METHOD

   4.1. Contour and scatter plot for method with constant step

   4.2. Contour and scatter plot for method with dynamic step

   4.3. Contour and scatter plot for fastest gradient descent

import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
import numpy as np
from IPython.display import display, Math, Latex
import pylab
import plot_methods
import optimization_methods
%matplotlib inline

Plot function graphic

my_function = lambda x, y: x**2+2*y**2+0.012*x*y-2*y+x

plot_methods.plot_function(my_function, 'My function')

Gradient descent

constant step

results_con_step = optimization_methods.gradient_descent_constant_step(my_function, [1,1], 1e-5, 0.0015)

number of iteration: 2, current point: [0.99097761 0.99398219], function value: 1.9728712043744712
number of iteration: 3, current point: [0.98648678 0.99100046], function value: 1.953537165405653
number of iteration: 4, current point: [0.98200949 0.9880367 ], function value: 1.9343548912118216
number of iteration: 5, current point: [0.97754567 0.9850908 ], function value: 1.9153230426242125
number of iteration: 6, current point: [0.9730953  0.98216266], function value: 1.896440293641402
number of iteration: 7, current point: [0.96865834 0.97925217], function value: 1.877705331288705
number of iteration: 8, current point: [0.96423474 0.97635922], function value: 1.8591168554787423
number of iteration: 9, current point: [0.95982446 0.97348371], function value: 1.8406735788748265
number of iteration: 10, current point: [0.95542746 0.97062553], function value: 1.822374226754802
number of iteration: 11, current point: [0.95104371 0.96778458], function value: 1.804217536877316
number of iteration: 12, current point: [0.94667316 0.96496075], function value: 1.786202259348535
number of iteration: 13, current point: [0.94231577 0.96215395], function value: 1.7683271564911212
number of iteration: 14, current point: [0.9379715  0.95936406], function value: 1.750591002714629
number of iteration: 15, current point: [0.93364032 0.956591  ], function value: 1.7329925843869756
number of iteration: 16, current point: [0.92932218 0.95383464], function value: 1.7155306997075725
number of iteration: 17, current point: [0.92501704 0.95109491], function value: 1.6982041585823082
number of iteration: 18, current point: [0.92072487 0.94837169], function value: 1.6810117824987438
number of iteration: 19, current point: [0.91644563 0.94566489], function value: 1.6639524044042426
number of iteration: 20, current point: [0.91217927 0.9429744 ], function value: 1.6470248685839581
number of iteration: 21, current point: [0.90792576 0.94030013], function value: 1.630228030541589
number of iteration: 22, current point: [0.90368506 0.93764199], function value: 1.613560756880287
number of iteration: 23, current point: [0.89945712 0.93499987], function value: 1.597021925185417
number of iteration: 24, current point: [0.89524192 0.93237368], function value: 1.580610423909397
number of iteration: 25, current point: [0.89103941 0.92976333], function value: 1.5643251522554924
number of iteration: 26, current point: [0.88684956 0.92716871], function value: 1.548165020065957
number of iteration: 27, current point: [0.88267232 0.92458973], function value: 1.5321289477094546
number of iteration: 28, current point: [0.87850766 0.92202631], function value: 1.5162158659695568
number of iteration: 29, current point: [0.87435554 0.91947834], function value: 1.500424715935762
number of iteration: 30, current point: [0.87021592 0.91694573], function value: 1.484754448895095
number of iteration: 31, current point: [0.86608877 0.91442839], function value: 1.4692040262249346
number of iteration: 32, current point: [0.86197405 0.91192623], function value: 1.4537724192863597
number of iteration: 33, current point: [0.85787171 0.90943916], function value: 1.438458609320127
number of iteration: 34, current point: [0.85378172 0.90696708], function value: 1.4232615873426906
number of iteration: 35, current point: [0.84970405 0.90450991], function value: 1.4081803540434352
number of iteration: 36, current point: [0.84563866 0.90206755], function value: 1.393213919683964
number of iteration: 37, current point: [0.84158551 0.89963993], function value: 1.3783613039971452
number of iteration: 38, current point: [0.83754456 0.89722694], function value: 1.3636215360886683
number of iteration: 39, current point: [0.83351577 0.8948285 ], function value: 1.3489936543384484
number of iteration: 40, current point: [0.82949912 0.89244453], function value: 1.334476706303883
number of iteration: 41, current point: [0.82549456 0.89007493], function value: 1.3200697486240327
number of iteration: 42, current point: [0.82150205 0.88771962], function value: 1.3057718469250466
number of iteration: 43, current point: [0.81752157 0.88537852], function value: 1.2915820757258971
number of iteration: 44, current point: [0.81355307 0.88305153], function value: 1.2774995183462052
number of iteration: 45, current point: [0.80959651 0.88073858], function value: 1.2635232668142549
number of iteration: 46, current point: [0.80565187 0.87843957], function value: 1.2496524217762475
number of iteration: 47, current point: [0.8017191  0.87615443], function value: 1.2358860924071418
number of iteration: 48, current point: [0.79779817 0.87388308], function value: 1.2222233963212505
number of iteration: 49, current point: [0.79388905 0.87162542], function value: 1.2086634594854573
number of iteration: 50, current point: [0.78999169 0.86938137], function value: 1.1952054161315875
number of iteration: 51, current point: [0.78610607 0.86715087], function value: 1.181848408670962
number of iteration: 52, current point: [0.78223214 0.86493381], function value: 1.1685915876100719
number of iteration: 53, current point: [0.77836988 0.86273013], function value: 1.1554341114661533
number of iteration: 54, current point: [0.77451924 0.86053974], function value: 1.142375146684349
number of iteration: 55, current point: [0.77068019 0.85836256], function value: 1.129413867555678
number of iteration: 56, current point: [0.7668527  0.85619851], function value: 1.11654945613606
number of iteration: 57, current point: [0.76303673 0.85404752], function value: 1.1037811021661987
number of iteration: 58, current point: [0.75923225 0.8519095 ], function value: 1.0911080029915072
number of iteration: 59, current point: [0.75543922 0.84978437], function value: 1.078529363484491
number of iteration: 60, current point: [0.7516576  0.84767207], function value: 1.0660443959666979
number of iteration: 61, current point: [0.74788737 0.84557251], function value: 1.053652320132007
number of iteration: 62, current point: [0.74412849 0.84348561], function value: 1.0413523629708685
number of iteration: 63, current point: [0.74038092 0.8414113 ], function value: 1.0291437586948515
number of iteration: 64, current point: [0.73664463 0.83934951], function value: 1.0170257486630134
number of iteration: 65, current point: [0.73291959 0.83730015], function value: 1.0049975813077374
number of iteration: 66, current point: [0.72920576 0.83526316], function value: 0.993058512062551
number of iteration: 67, current point: [0.72550311 0.83323845], function value: 0.9812078032904217
number of iteration: 68, current point: [0.7218116  0.83122596], function value: 0.9694447242121753
number of iteration: 69, current point: [0.7181312  0.82922561], function value: 0.9577685508367713
number of iteration: 70, current point: [0.71446188 0.82723733], function value: 0.9461785658913524
number of iteration: 71, current point: [0.71080361 0.82526105], function value: 0.9346740587529114
number of iteration: 72, current point: [0.70715634 0.82329669], function value: 0.923254325379971
number of iteration: 73, current point: [0.70352005 0.82134418], function value: 0.9119186682455978
number of iteration: 74, current point: [0.69989471 0.81940345], function value: 0.90066639627073
number of iteration: 75, current point: [0.69628028 0.81747443], function value: 0.8894968247585182
number of iteration: 76, current point: [0.69267672 0.81555705], function value: 0.8784092753292185
number of iteration: 77, current point: [0.68908401 0.81365124], function value: 0.8674030758558033
number of iteration: 78, current point: [0.68550211 0.81175693], function value: 0.8564775604002601
number of iteration: 79, current point: [0.68193099 0.80987405], function value: 0.8456320691509156
number of iteration: 80, current point: [0.67837062 0.80800253], function value: 0.834865948359844
number of iteration: 81, current point: [0.67482097 0.80614231], function value: 0.8241785502814734
number of iteration: 82, current point: [0.67128199 0.8042933 ], function value: 0.8135692331115767
number of iteration: 83, current point: [0.66775367 0.80245546], function value: 0.8030373609272152
number of iteration: 84, current point: [0.66423597 0.80062871], function value: 0.7925823036267958
number of iteration: 85, current point: [0.66072885 0.79881298], function value: 0.7822034368715085
number of iteration: 86, current point: [0.65723228 0.79700821], function value: 0.7719001420267366
number of iteration: 87, current point: [0.65374624 0.79521433], function value: 0.761671806104437
number of iteration: 88, current point: [0.65027069 0.79343128], function value: 0.7515178217062235
number of iteration: 89, current point: [0.64680559 0.79165898], function value: 0.7414375869668532
number of iteration: 90, current point: [0.64335093 0.78989739], function value: 0.7314305054984847
number of iteration: 91, current point: [0.63990665 0.78814642], function value: 0.7214959863352892
number of iteration: 92, current point: [0.63647275 0.78640603], function value: 0.7116334438790322
number of iteration: 93, current point: [0.63304917 0.78467613], function value: 0.7018422978450269
number of iteration: 94, current point: [0.6296359  0.78295668], function value: 0.6921219732085122
number of iteration: 95, current point: [0.6262329  0.78124761], function value: 0.6824719001521746
number of iteration: 96, current point: [0.62284014 0.77954885], function value: 0.6728915140135243
number of iteration: 97, current point: [0.61945759 0.77786035], function value: 0.6633802552333119
number of iteration: 98, current point: [0.61608521 0.77618203], function value: 0.6539375693043157
number of iteration: 99, current point: [0.61272299 0.77451385], function value: 0.6445629067208736
number of iteration: 100, current point: [0.60937088 0.77285574], function value: 0.6352557229286764
number of iteration: 101, current point: [0.60602885 0.77120764], function value: 0.626015478275316
number of iteration: 102, current point: [0.60269688 0.76956948], function value: 0.6168416379613264
number of iteration: 103, current point: [0.59937494 0.76794122], function value: 0.6077336719916824
number of iteration: 104, current point: [0.59606299 0.76632278], function value: 0.5986910551278777
number of iteration: 105, current point: [0.59276101 0.76471412], function value: 0.5897132668405429
number of iteration: 106, current point: [0.58946896 0.76311516], function value: 0.5807997912625693
number of iteration: 107, current point: [0.58618682 0.76152586], function value: 0.5719501171424528
number of iteration: 108, current point: [0.58291455 0.75994615], function value: 0.5631637377987946
number of iteration: 109, current point: [0.57965213 0.75837598], function value: 0.5544401510746035
number of iteration: 110, current point: [0.57639952 0.75681529], function value: 0.5457788592924535
number of iteration: 111, current point: [0.5731567  0.75526403], function value: 0.537179369210125
number of iteration: 112, current point: [0.56992364 0.75372213], function value: 0.5286411919764769
number of iteration: 113, current point: [0.5667003  0.75218954], function value: 0.5201638430880928
number of iteration: 114, current point: [0.56348666 0.7506662 ], function value: 0.5117468423462526
number of iteration: 115, current point: [0.56028269 0.74915206], function value: 0.5033897138142345
number of iteration: 116, current point: [0.55708835 0.74764706], function value: 0.4950919857754341
number of iteration: 117, current point: [0.55390363 0.74615115], function value: 0.486853190691408
number of iteration: 118, current point: [0.55072849 0.74466427], function value: 0.4786728651609711
number of iteration: 119, current point: [0.5475629  0.74318637], function value: 0.47055054987920975
number of iteration: 120, current point: [0.54440683 0.7417174 ], function value: 0.46248578959736464
number of iteration: 121, current point: [0.54126026 0.7402573 ], function value: 0.4544781330825636
number of iteration: 122, current point: [0.53812316 0.73880601], function value: 0.4465271330787788
number of iteration: 123, current point: [0.53499549 0.73736349], function value: 0.43863234626736336
number of iteration: 124, current point: [0.53187723 0.73592968], function value: 0.4307933332286862
number of iteration: 125, current point: [0.52876835 0.73450452], function value: 0.42300965840384075
number of iteration: 126, current point: [0.52566883 0.73308798], function value: 0.4152808900567371
number of iteration: 127, current point: [0.52257862 0.73167999], function value: 0.40760660023679995
number of iteration: 128, current point: [0.51949772 0.7302805 ], function value: 0.39998636474177074
number of iteration: 129, current point: [0.51642608 0.72888947], function value: 0.3924197630812414
number of iteration: 130, current point: [0.51336368 0.72750684], function value: 0.38490637844046893
number of iteration: 131, current point: [0.51031049 0.72613256], function value: 0.37744579764430775
number of iteration: 132, current point: [0.50726649 0.72476657], function value: 0.37003761112182887
number of iteration: 133, current point: [0.50423165 0.72340884], function value: 0.36268141287133004
number of iteration: 134, current point: [0.50120593 0.72205931], function value: 0.3553768004253748
number of iteration: 135, current point: [0.49818932 0.72071794], function value: 0.3481233748166408
number of iteration: 136, current point: [0.49518178 0.71938466], function value: 0.3409207405438507
number of iteration: 137, current point: [0.49218328 0.71805944], function value: 0.333768505538101
number of iteration: 138, current point: [0.48919381 0.71674223], function value: 0.3266662811296396
number of iteration: 139, current point: [0.48621332 0.71543297], function value: 0.3196136820149924
number of iteration: 140, current point: [0.48324181 0.71413162], function value: 0.31261032622415186
number of iteration: 141, current point: [0.48027923 0.71283813], function value: 0.3056558350885128
number of iteration: 142, current point: [0.47732556 0.71155245], function value: 0.2987498332090611
number of iteration: 143, current point: [0.47438077 0.71027455], function value: 0.2918919484246214
number of iteration: 144, current point: [0.47144485 0.70900436], function value: 0.2850818117806361
number of iteration: 145, current point: [0.46851775 0.70774185], function value: 0.27831905749841224
number of iteration: 146, current point: [0.46559946 0.70648697], function value: 0.27160332294453415
number of iteration: 147, current point: [0.46268994 0.70523966], function value: 0.26493424860036274
number of iteration: 148, current point: [0.45978918 0.7039999 ], function value: 0.25831147803238974
number of iteration: 149, current point: [0.45689714 0.70276762], function value: 0.25173465786249305
number of iteration: 150, current point: [0.4540138  0.70154279], function value: 0.2452034377386071
number of iteration: 151, current point: [0.45113913 0.70032536], function value: 0.23871747030573287
number of iteration: 152, current point: [0.4482731  0.69911529], function value: 0.23227641117720677
number of iteration: 153, current point: [0.4454157  0.69791253], function value: 0.22587991890645154
number of iteration: 154, current point: [0.44256689 0.69671704], function value: 0.21952765495868853
number of iteration: 155, current point: [0.43972665 0.69552877], function value: 0.21321928368321297
number of iteration: 156, current point: [0.43689495 0.69434768], function value: 0.20695447228583774
number of iteration: 157, current point: [0.43407177 0.69317373], function value: 0.20073289080168744
number of iteration: 158, current point: [0.43125707 0.69200687], function value: 0.1945542120682674
number of iteration: 159, current point: [0.42845085 0.69084707], function value: 0.18841811169885392
number of iteration: 160, current point: [0.42565306 0.68969428], function value: 0.182324268055848
number of iteration: 161, current point: [0.42286369 0.68854845], function value: 0.1762723622250273
number of iteration: 162, current point: [0.4200827  0.68740955], function value: 0.17026207798941806
number of iteration: 163, current point: [0.41731008 0.68627753], function value: 0.16429310180389067
number of iteration: 164, current point: [0.4145458  0.68515235], function value: 0.1583651227697166
number of iteration: 165, current point: [0.41178983 0.68403397], function value: 0.15247783260968872
number of iteration: 166, current point: [0.40904214 0.68292236], function value: 0.14663092564316094
number of iteration: 167, current point: [0.40630272 0.68181746], function value: 0.14082409876164448
number of iteration: 168, current point: [0.40357154 0.68071924], function value: 0.13505705140447943
number of iteration: 169, current point: [0.40084858 0.67962766], function value: 0.12932948553488166
number of iteration: 170, current point: [0.3981338  0.67854268], function value: 0.12364110561605746
number of iteration: 171, current point: [0.39542718 0.67746426], function value: 0.11799161858779672
number of iteration: 172, current point: [0.39272871 0.67639236], function value: 0.11238073384307434
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number of iteration: 1914, current point: [-0.49823699  0.50148544], function value: -0.7529907818405948
number of iteration: 1915, current point: [-0.4982513  0.5014855], function value: -0.7529909182654636
number of iteration: 1916, current point: [-0.49826557  0.50148555], function value: -0.7529910538730369
number of iteration: 1917, current point: [-0.4982798   0.50148561], function value: -0.7529911886682106
number of iteration: 1918, current point: [-0.49829399  0.50148566], function value: -0.7529913226558522
number of iteration: 1919, current point: [-0.49830814  0.50148572], function value: -0.752991455840799
number of iteration: 1920, current point: [-0.49832224  0.50148577], function value: -0.7529915882278598
number of iteration: 1921, current point: [-0.4983363   0.50148583], function value: -0.7529917198218151
number of iteration: 1922, current point: [-0.49835032  0.50148588], function value: -0.7529918506274158
number of iteration: 1923, current point: [-0.49836429  0.50148594], function value: -0.7529919806493853
number of iteration: 1924, current point: [-0.49837823  0.50148599], function value: -0.7529921098924177
number of iteration: 1925, current point: [-0.49839212  0.50148605], function value: -0.7529922383611796
number of iteration: 1926, current point: [-0.49840597  0.5014861 ], function value: -0.7529923660603095
number of iteration: 1927, current point: [-0.49841978  0.50148616], function value: -0.7529924929944182
number of iteration: 1928, current point: [-0.49843354  0.50148621], function value: -0.7529926191680889
number of iteration: 1929, current point: [-0.49844727  0.50148627], function value: -0.7529927445858772
number of iteration: 1930, current point: [-0.49846096  0.50148632], function value: -0.7529928692523116
number of iteration: 1931, current point: [-0.4984746   0.50148638], function value: -0.7529929931718932
number of iteration: 1932, current point: [-0.4984882   0.50148643], function value: -0.7529931163490962
number of iteration: 1933, current point: [-0.49850176  0.50148648], function value: -0.752993238788368
number of iteration: 1934, current point: [-0.49851529  0.50148654], function value: -0.7529933604941297
number of iteration: 1935, current point: [-0.49852877  0.50148659], function value: -0.7529934814707756
number of iteration: 1936, current point: [-0.49854221  0.50148665], function value: -0.7529936017226734
number of iteration: 1937, current point: [-0.49855561  0.5014867 ], function value: -0.7529937212541651
number of iteration: 1938, current point: [-0.49856897  0.50148675], function value: -0.7529938400695668
number of iteration: 1939, current point: [-0.49858229  0.50148681], function value: -0.7529939581731679
number of iteration: 1940, current point: [-0.49859557  0.50148686], function value: -0.7529940755692334
number of iteration: 1941, current point: [-0.49860881  0.50148692], function value: -0.7529941922620015
number of iteration: 1942, current point: [-0.49862201  0.50148697], function value: -0.7529943082556858
number of iteration: 1943, current point: [-0.49863517  0.50148702], function value: -0.7529944235544743
number of iteration: 1944, current point: [-0.49864829  0.50148708], function value: -0.7529945381625299
number of iteration: 1945, current point: [-0.49866137  0.50148713], function value: -0.7529946520839907
number of iteration: 1946, current point: [-0.49867441  0.50148718], function value: -0.75299476532297
number of iteration: 1947, current point: [-0.49868742  0.50148723], function value: -0.7529948778835566
number of iteration: 1948, current point: [-0.49870038  0.50148729], function value: -0.7529949897698145
number of iteration: 1949, current point: [-0.49871331  0.50148734], function value: -0.7529951009857834
number of iteration: 1950, current point: [-0.49872619  0.50148739], function value: -0.752995211535479
number of iteration: 1951, current point: [-0.49873904  0.50148745], function value: -0.7529953214228928
number of iteration: 1952, current point: [-0.49875185  0.5014875 ], function value: -0.7529954306519923
number of iteration: 1953, current point: [-0.49876462  0.50148755], function value: -0.7529955392267217
number of iteration: 1954, current point: [-0.49877736  0.5014876 ], function value: -0.7529956471510009
number of iteration: 1955, current point: [-0.49879005  0.50148766], function value: -0.7529957544287266
number of iteration: 1956, current point: [-0.49880271  0.50148771], function value: -0.7529958610637721
number of iteration: 1957, current point: [-0.49881533  0.50148776], function value: -0.7529959670599882
number of iteration: 1958, current point: [-0.49882791  0.50148781], function value: -0.7529960724212013
number of iteration: 1959, current point: [-0.49884045  0.50148786], function value: -0.752996177151216
number of iteration: 1960, current point: [-0.49885296  0.50148792], function value: -0.7529962812538136
number of iteration: 1961, current point: [-0.49886542  0.50148797], function value: -0.7529963847327531
number of iteration: 1962, current point: [-0.49887785  0.50148802], function value: -0.7529964875917703
number of iteration: 1963, current point: [-0.49889025  0.50148807], function value: -0.752996589834579
number of iteration: 1964, current point: [-0.4989026   0.50148812], function value: -0.7529966914648712
number of iteration: 1965, current point: [-0.49891492  0.50148818], function value: -0.7529967924863161
number of iteration: 1966, current point: [-0.4989272   0.50148823], function value: -0.7529968929025613
number of iteration: 1967, current point: [-0.49893945  0.50148828], function value: -0.7529969927172323
number of iteration: 1968, current point: [-0.49895166  0.50148833], function value: -0.7529970919339335
number of iteration: 1969, current point: [-0.49896383  0.50148838], function value: -0.7529971905562467
number of iteration: 1970, current point: [-0.49897597  0.50148843], function value: -0.752997288587733
number of iteration: 1971, current point: [-0.49898806  0.50148848], function value: -0.7529973860319317
number of iteration: 1972, current point: [-0.49900013  0.50148853], function value: -0.7529974828923615
number of iteration: 1973, current point: [-0.49901215  0.50148858], function value: -0.7529975791725193
number of iteration: 1974, current point: [-0.49902414  0.50148863], function value: -0.7529976748758818
number of iteration: 1975, current point: [-0.4990361   0.50148869], function value: -0.7529977700059043
number of iteration: 1976, current point: [-0.49904802  0.50148874], function value: -0.7529978645660214
number of iteration: 1977, current point: [-0.4990599   0.50148879], function value: -0.7529979585596477
number of iteration: 1978, current point: [-0.49907175  0.50148884], function value: -0.7529980519901767
number of iteration: 1979, current point: [-0.49908356  0.50148889], function value: -0.7529981448609815
number of iteration: 1980, current point: [-0.49909533  0.50148894], function value: -0.7529982371754158
number of iteration: 1981, current point: [-0.49910707  0.50148899], function value: -0.7529983289368124
number of iteration: 1982, current point: [-0.49911878  0.50148904], function value: -0.7529984201484847
number of iteration: 1983, current point: [-0.49913045  0.50148909], function value: -0.7529985108137259
number of iteration: 1984, current point: [-0.49914209  0.50148914], function value: -0.7529986009358097
number of iteration: 1985, current point: [-0.49915369  0.50148919], function value: -0.7529986905179897
number of iteration: 1986, current point: [-0.49916525  0.50148924], function value: -0.7529987795635007
number of iteration: 1987, current point: [-0.49917678  0.50148929], function value: -0.7529988680755577
number of iteration: 1988, current point: [-0.49918828  0.50148934], function value: -0.7529989560573564
number of iteration: 1989, current point: [-0.49919974  0.50148938], function value: -0.7529990435120735
number of iteration: 1990, current point: [-0.49921117  0.50148943], function value: -0.7529991304428669
number of iteration: 1991, current point: [-0.49922256  0.50148948], function value: -0.7529992168528751
number of iteration: 1992, current point: [-0.49923392  0.50148953], function value: -0.7529993027452181
number of iteration: 1993, current point: [-0.49924525  0.50148958], function value: -0.752999388122997
number of iteration: 1994, current point: [-0.49925654  0.50148963], function value: -0.7529994729892947
number of iteration: 1995, current point: [-0.4992678   0.50148968], function value: -0.7529995573471754
number of iteration: 1996, current point: [-0.49927902  0.50148973], function value: -0.7529996411996847
number of iteration: 1997, current point: [-0.49929021  0.50148978], function value: -0.7529997245498502
number of iteration: 1998, current point: [-0.49930136  0.50148983], function value: -0.7529998074006815
number of iteration: 1999, current point: [-0.49931249  0.50148987], function value: -0.75299988975517
number of iteration: 2000, current point: [-0.49932358  0.50148992], function value: -0.7529999716162891
number of iteration: 2001, current point: [-0.49933463  0.50148997], function value: -0.7530000529869946
number of iteration: 2002, current point: [-0.49934566  0.50149002], function value: -0.7530001338702245
number of iteration: 2003, current point: [-0.49935665  0.50149007], function value: -0.7530002142688991
number of iteration: 2004, current point: [-0.4993676   0.50149011], function value: -0.7530002941859213
number of iteration: 2005, current point: [-0.49937853  0.50149016], function value: -0.7530003736241766
number of iteration: 2006, current point: [-0.49938942  0.50149021], function value: -0.7530004525865331
number of iteration: 2007, current point: [-0.49940028  0.50149026], function value: -0.7530005310758421
number of iteration: 2008, current point: [-0.4994111   0.50149031], function value: -0.7530006090949373
number of iteration: 2009, current point: [-0.4994219   0.50149035], function value: -0.7530006866466357
number of iteration: 2010, current point: [-0.49943266  0.5014904 ], function value: -0.7530007637337373
number of iteration: 2011, current point: [-0.49944339  0.50149045], function value: -0.7530008403590256
number of iteration: 2012, current point: [-0.49945408  0.5014905 ], function value: -0.7530009165252671
number of iteration: 2013, current point: [-0.49946475  0.50149054], function value: -0.7530009922352119
number of iteration: 2014, current point: [-0.49947538  0.50149059], function value: -0.7530010674915937
number of iteration: 2015, current point: [-0.49948598  0.50149064], function value: -0.7530011422971297
number of iteration: 2016, current point: [-0.49949655  0.50149068], function value: -0.7530012166545204
number of iteration: 2017, current point: [-0.49950709  0.50149073], function value: -0.7530012905664512
number of iteration: 2018, current point: [-0.49951759  0.50149078], function value: -0.7530013640355903
number of iteration: 2019, current point: [-0.49952807  0.50149082], function value: -0.7530014370645906
number of iteration: 2020, current point: [-0.49953851  0.50149087], function value: -0.7530015096560888
number of iteration: 2021, current point: [-0.49954892  0.50149092], function value: -0.7530015818127059
number of iteration: 2022, current point: [-0.4995593   0.50149096], function value: -0.7530016535370474
number of iteration: 2023, current point: [-0.49956965  0.50149101], function value: -0.7530017248317029
number of iteration: 2024, current point: [-0.49957997  0.50149106], function value: -0.7530017956992462
number of iteration: 2025, current point: [-0.49959025  0.5014911 ], function value: -0.7530018661422364
number of iteration: 2026, current point: [-0.49960051  0.50149115], function value: -0.753001936163217
number of iteration: 2027, current point: [-0.49961074  0.50149119], function value: -0.7530020057647159
number of iteration: 2028, current point: [-0.49962093  0.50149124], function value: -0.7530020749492463
number of iteration: 2029, current point: [-0.49963109  0.50149129], function value: -0.7530021437193062
number of iteration: 2030, current point: [-0.49964123  0.50149133], function value: -0.7530022120773784
number of iteration: 2031, current point: [-0.49965133  0.50149138], function value: -0.7530022800259313
number of iteration: 2032, current point: [-0.4996614   0.50149142], function value: -0.7530023475674181
number of iteration: 2033, current point: [-0.49967145  0.50149147], function value: -0.7530024147042775
number of iteration: 2034, current point: [-0.49968146  0.50149151], function value: -0.7530024814389336
number of iteration: 2035, current point: [-0.49969144  0.50149156], function value: -0.7530025477737959
Precision: 9.982573116418513e-06

dynamic step

results_dyn_step = optimization_methods.gradient_descent(my_function, [1,1], 1e-5)

number of iteration: 2, current point: [-0.506 -0.006], function value: -0.23785556799289725
number of iteration: 3, current point: [-0.502982  0.501518], function value: -0.7530135533481125
number of iteration: 4, current point: [-0.50300911  0.50149989], function value: -0.7530135540770652
number of iteration: 5, current point: [-0.50300905  0.50150903], function value: -0.7530135542439764
Precision: 1.1762602059271537e-09

swift-gradient

results_swift_grad = optimization_methods.gradient_descend_swift(my_function, [1,1], 1e-5, method='golden_ratio')

number of iteration: 2, current point: [-0.1460417   0.23445023], function value: -0.4840910377119281
number of iteration: 3, current point: [-0.3568258  0.5499907], function value: -0.7268580199452551
number of iteration: 4, current point: [-0.46829201  0.47553453], function value: -0.7504697534627472
number of iteration: 5, current point: [-0.48879192  0.50622443], function value: -0.7527661528908174
number of iteration: 6, current point: [-0.49963246  0.49898283], function value: -0.7529894918392976
number of iteration: 7, current point: [-0.50162629  0.50196763], function value: -0.7530112139608441
number of iteration: 8, current point: [-0.50268065  0.50126334], function value: -0.753013326632081
number of iteration: 9, current point: [-0.50287457  0.50155363], function value: -0.7530135321061622
number of iteration: 10, current point: [-0.50297712  0.50148513], function value: -0.753013552090942
number of iteration: 11, current point: [-0.50299598  0.50151337], function value: -0.7530135540345996
number of iteration: 12, current point: [-0.50300594  0.5015067 ], function value: -0.7530135542235831
number of iteration: 13, current point: [-0.50300779  0.50150946], function value: -0.7530135542419912
Precision: 3.076604076091895e-06

Contour

plot_methods.plot_contour(my_function, 'Contour')

Contour and Scatter

constant step contour

plot_methods.plot_contour_and_scatter_of_descent(my_function, results_con_step, 
                                                 'Contour and Scatter constant step')

dynamic step contour

plot_methods.plot_contour_and_scatter_of_descent(my_function, results_dyn_step, 
                                                 'Contour and Scatter dynamic step')

fastest descent contour

plot_methods.plot_contour_and_scatter_of_descent(my_function, results_swift_grad, 
                                                 'Contour and Scatter fastest gradient descent')